Question

find the value of y if the line through the two given points is to have the indicated slope. (-3,y) and (-11,8), m = -2

Answer 1

$\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{y})\qquad(\stackrel{x_2}{-11}~,~\stackrel{y_2}{8})\\\\\\slope = m\implies\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{8-y}{-11-(-3)}~~=~~\stackrel{m}{-2}\\\\\\\cfrac{8-y}{-11+3}=-2\implies \cfrac{8-y}{-8}=-2\implies 8-y=16\implies -8=y$

Answer 2

$= \frac{y - y_{2}}{x - x _{2}} \\ - 2 = \frac{y - ( - 11)}{ - 3 - 8} \\ - 2 = \frac{y + 11}{ - 11} \\ - 2 + 1 = y \\ y = - 1$